ON THE REFLEXION AND REFEACTION OF LIGHT. 249 



the forces in nature are so disposed as to render this a natural 

 impossibility. 



Let us now take any element of the medium, rectangular 

 in a state of repose, and of which the sides are dx, dy, dz ; the 

 length of the sides composed of the same particles will in a 

 state of motion become 



dx=dx (1 +*,), dy=dy (1 +* a )> dz =dz (1 +s s ) ; 



where s l , s 2 , s 3 are exceedingly small quantities of the first order. 

 If, moreover, we make, 



a, /3, and y will be very small quantities of the same order. 

 But, whatever may be the nature of the internal actions, if we 

 represent by 



&</> dx dy dz, 



the part of the second member of the equation (1), due to the 

 molecules in the element under consideration, it is evident, 

 that <f> will remain the same when all the sides and all the 

 angles of the parallelepiped, whose sides are dx dy dz, remain 

 unaltered, and therefore its most general value must be of the 

 form 



= function fo, *, * a , a, & y]. 



~^~ 



But 5 X , 5 2 , s 3 , a, /3, y being very small quantities of the 

 first order, we may expand <j> in a very convergent series of 

 the form 



< , (f) l} < 2 , &c. being homogeneous functions of the six quan- 

 tities a, /3, y, $ t , s a , s s of the degrees 0, 1, 2, &c. each of which 

 is very great compared with the next following one. If now, p 

 represent the primitive density of the element dx dy dz, we may 

 write p dxdy dz in the place of Dm in the formula (1), which 

 will thus become, since </> is constant, 



